
/* @(#)w_j0.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/*
 * wrapper fd_j0(double x), fd_y0(double x)
 */

#include "fdlibm.h"
#include "fdlibm_intern.h"

static double pzero(double), qzero(double);

static const double
 		/* R0/S0 on [0, 2.00] */
R02  =  1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
R03  = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
R04  =  1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
R05  = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
S01  =  1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
S02  =  1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
S03  =  5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
S04  =  1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */

static const double
u00  = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
u01  =  1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
u02  = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
u03  =  3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
u04  = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
u05  =  1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
u06  = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
v01  =  1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
v02  =  7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
v03  =  2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
v04  =  4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */


double fd_j0(double x)		/* wrapper fd_j0 */
{
	double z, s,c,ss,cc,r,u,v;
	int hx,ix;

	hx = FD_HI(x);
	ix = hx&0x7fffffff;
	if(ix>=0x7ff00000) return gD(one, gM(x,x));
	x = fd_fabs(x);
	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
		s = fd_sin(x);
		c = fd_cos(x);
		ss = gS(s,c);
		cc = gA(s,c);
		if(ix<0x7fe00000) {  /* make sure x+x not overflow */
		    z = -fd_cos(gA(x,x));
		    if (gM(s,c) < zero) cc = gD(z,ss);
		    else 	    ss = gD(z,cc);
		}
	/*
	 * fd_j0(x) = 1/fd_sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / fd_sqrt(x)
	 * fd_y0(x) = 1/fd_sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / fd_sqrt(x)
	 */
		if(ix>0x48000000) z = gD(gM(invsqrtpi,cc),gSqrt(x));
		else {
		    u = pzero(x); v = qzero(x);
		    z = gD(gM(invsqrtpi, (gS(gM(u,cc), gM(v,ss)))), gSqrt(x));
		}
		return z;
	}
	if(ix<0x3f200000) {	/* |x| < 2**-13 */
	    if(huge+x>one) {	/* raise inexact if x != 0 */
	        if(ix<0x3e400000) return one;	/* |x|<2**-27 */
	        else 	      return gS(one, gM(gM(0.25,x),x));
	    }
	}
	z = gM(x,x);
	r = gM(z,gA(R02, gM(z,gA(R03, gM(z,gA(R04, gM(z,R05)))))));
	s = gA(one, gM(z,gA(S01, gM(z,gA(S02, gM(z,gA(S03, gM(z,S04))))))));
	if(ix < 0x3FF00000) {	/* |x| < 1.00 */
	    return gA(one, gM(z,gA(-0.25,gD(r,s))));
	} else {
	    u = gM(0.5,x);
	    return(gM(gA(one, u), gS(one, u)) + gM(z, gD(r,s)));
	}
}

double fd_y0(double x)		/* wrapper fd_y0 */
{
	double z, s,c,ss,cc,u,v;
	int hx,ix,lx;

        hx = FD_HI(x);
        ix = 0x7fffffff&hx;
        lx = FD_LO(x);
    /* Y0(NaN) is NaN, fd_y0(-inf) is Nan, fd_y0(inf) is 0  */
	if(ix>=0x7ff00000) return gD( one, gA(x, gM(x,x)));
        if((ix|lx)==0) return gD(-one, zero);
        if(hx<0) return gD(zero,zero);
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
        /* fd_y0(x) = fd_sqrt(2/(pi*x))*(p0(x)*fd_sin(x0)+q0(x)*fd_cos(x0))
         * where x0 = x-pi/4
         *      Better formula:
         *              fd_cos(x0) = fd_cos(x)fd_cos(pi/4)+fd_sin(x)fd_sin(pi/4)
         *                      =  1/fd_sqrt(2) * (fd_sin(x) + fd_cos(x))
         *              fd_sin(x0) = fd_sin(x)fd_cos(3pi/4)-fd_cos(x)fd_sin(3pi/4)
         *                      =  1/fd_sqrt(2) * (fd_sin(x) - fd_cos(x))
         * To avoid cancellation, use
         *              fd_sin(x) +- fd_cos(x) = -fd_cos(2x)/(fd_sin(x) -+ fd_cos(x))
         * to compute the worse one.
         */
                s = fd_sin(x);
                c = fd_cos(x);
                ss = gS(s,c);
                cc = gA(s,c);
	/*
	 * fd_j0(x) = 1/fd_sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / fd_sqrt(x)
	 * fd_y0(x) = 1/fd_sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / fd_sqrt(x)
	 */
                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
                    z = -fd_cos(gA(x,x));
                    if (gM(s,c) < zero) cc = gD(z,ss);
                    else            ss = gD(z,cc);
                }
                if(ix>0x48000000) z = gD(gM(invsqrtpi,ss), gSqrt(x));
                else {
                    u = pzero(x); v = qzero(x);
                    z = gD(gM(invsqrtpi, gA(gM(u,ss), gM(v,cc))), gSqrt(x));
                }
                return z;
	}
	if(ix<=0x3e400000) {	/* x < 2**-27 */
	    return gA(u00, gM(tpi, fd_log(x)));
	}
	z = gM(x,x);
	u = gA(u00, gM(z,gA(u01, gM(z,gA(u02, gM(z,gA(u03, gM(z,gA(u04, gM(z,gA(u05, gM(z,u06))))))))))));
	v = gA(one, gM(z,gA(v01, gM(z,gA(v02, gM(z,gA(v03, gM(z,v04))))))));
	return(gD(u,v) + gM(tpi,gM(fd_j0(x), fd_log(x))));
}


/* The asymptotic expansions of pzero is
 *	1 - 9/128 s^2 + 11025/98304 s^4 - ...,	where s = 1/x.
 * For x >= 2, We approximate pzero by
 * 	pzero(x) = 1 + (R/S)
 * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
 * 	  S = 1 + pS0*s^2 + ... + pS4*s^10
 * and
 *	| pzero(x)-1-R/S | <= 2  ** ( -60.26)
 */
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
 -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
 -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
 -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
 -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
 -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
};

static const double pS8[5] = {
  1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
  3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
  4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
  1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
  4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
};

static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
 -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
 -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
 -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
 -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
 -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
 -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
};

static const double pS5_[5] = {
  6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
  1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
  5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
  9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
  2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
};

static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
 -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
 -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
 -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
 -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
 -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
 -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
};

static const double pS3_[5] = {
  3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
  3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
  1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
  1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
  1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
};

static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
 -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
 -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
 -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
 -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
 -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
 -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
};

static const double pS2_[5] = {
  2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
  1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
  2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
  1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
  1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
};

static double pzero(double x)
{
	const double *p,*q;
	double z,r,s;
	int ix;
	ix = 0x7fffffff&FD_HI(x);
	if(ix>=0x40200000)     {p = pR8; q= pS8;}
	else if(ix>=0x40122E8B){p = pR5; q= pS5_;}
	else if(ix>=0x4006DB6D){p = pR3; q= pS3_;}
	else if(ix>=0x40000000){p = pR2; q= pS2_;}
	z = gD(one, gM(x,x));
	r = gA(p[0], gM(z,gA(p[1], gM(z,gA(p[2], gM(z,gA(p[3], gM(z,gA(p[4], gM(z,p[5]))))))))));
	s = gA(one , gM(z,gA(q[0], gM(z,gA(q[1], gM(z,gA(q[2], gM(z,gA(q[3], gM(z,q[4]))))))))));
	return gA(one, gD(r,s));
}


/* For x >= 8, the asymptotic expansions of qzero is
 *	-1/8 s + 75/1024 s^3 - ..., where s = 1/x.
 * We approximate pzero by
 * 	qzero(x) = s*(-1.25 + (R/S))
 * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
 * 	  S = 1 + qS0*s^2 + ... + qS5*s^12
 * and
 *	| qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
 */
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
  1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
  5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
  8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
  3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
};

static const double qS8[6] = {
  1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
  8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
  1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
  8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
  8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
 -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
};

static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
  7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
  5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
  1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
  1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
  1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
};

static const double qS5[6] = {
  8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
  2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
  1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
  5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
  3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
 -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
};

static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
  7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
  3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
  4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
  1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
  1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
};

static const double qS3_[6] = {
  4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
  7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
  3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
  6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
  2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
 -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
};

static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
  7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
  1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
  1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
  3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
  1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
};

static const double qS2_[6] = {
  3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
  2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
  8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
  8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
  2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
 -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
};

static double qzero(double x)
{
	const double *p,*q;
	double s,r,z;
	int ix;
	ix = 0x7fffffff&FD_HI(x);
	if(ix>=0x40200000)     {p = qR8; q= qS8;}
	else if(ix>=0x40122E8B){p = qR5; q= qS5;}
	else if(ix>=0x4006DB6D){p = qR3; q= qS3_;}
	else if(ix>=0x40000000){p = qR2; q= qS2_;}
	z = gD(one, gM(x,x));
	r = gA(p[0], gM(z,gA(p[1], gM(z,gA(p[2], gM(z,gA(p[3], gM(z,gA(p[4], gM(z,p[5]))))))))));
	s = gA(one , gM(z,gA(q[0], gM(z,gA(q[1], gM(z,gA(q[2], gM(z,gA(q[3], gM(z,gA(q[4], gM(z,q[5]))))))))))));
	return gD(gA(-.125, gD(r,s)), x);
}
